For quick, high luck dice rolling fun you need to try King of Tokyo. Giant monsters/robots battle to control Tokyo. This one, more than any other game has gotten my non-gamer house mates to the table.

Carcassonne is played almost exclusively 2 player in my house. One of the things that impresses me most about the game is how after my repeatedly trouncing my girlfriend she got hold of the app, trained up and brought the win/loss ratio up to 50%. It really isn't all about lucky tile draws.